Convert the 1000 0000 0000 1111 signed binary number to decimal number. A. 15 B. -15 C. -30 D. 30 E. None of the above

15
-15
-30
30 E. None of the above

The correct answer is $\boxed{\text{B) }-15}$.

To convert a binary number to decimal, you can use the following steps:

  1. Starting from the right, multiply each digit by 2 raised to the power of its position, starting with 0 for the rightmost digit.
  2. Add the products together.
  3. If the number is negative, add 1 to the result.

In this case, the binary number is $1000000000001111$.

  1. The rightmost digit is 1, so we multiply it by 2 to the power of 0, which is 1.
  2. The next digit is 0, so we multiply it by 2 to the power of 1, which is 2.
  3. The next digit is 0, so we multiply it by 2 to the power of 2, which is 4.
  4. The next digit is 0, so we multiply it by 2 to the power of 3, which is 8.
  5. The next digit is 0, so we multiply it by 2 to the power of 4, which is 16.
  6. The next digit is 1, so we multiply it by 2 to the power of 5, which is 32.
  7. The next digit is 1, so we multiply it by 2 to the power of 6, which is 64.
  8. The next digit is 1, so we multiply it by 2 to the power of 7, which is 128.
  9. The next digit is 1, so we multiply it by 2 to the power of 8, which is 256.
  10. The next digit is 1, so we multiply it by 2 to the power of 9, which is 512.
  11. The next digit is 1, so we multiply it by 2 to the power of 10, which is 1024.

Adding the products together, we get $1000000000001111 = -15$.

Since the number is negative, we add 1 to the result to get $-15 + 1 = \boxed{\text{B) }-15}$.

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